curve #5600

y² + y = x³ + 19322000426713381

a-invariants: [0, 0, 1, 0, 19322000426713381]
c-invariants: [0, -16694208368680361400]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 131659388254401650311201474884075
discriminant (Δ): -161282750611642021631221806732991875
Faltings height: 5.4346
naive height: 88.5232
primes of bad reduction: 3, 5, 7, 63092246291309
regulator: 260653634845057813.882724241685114644552254170911100357892264
submitted by: jesper-petersen
submitted at: 2026-10-23 21:44:04 UTC
last updated: 2026-10-23 21:44:04 UTC

Witness: 11 independent points log in to add more points →

(-380255146665271/1572598336, 4490360362607059685509/62362959612416)
(10056585383788561/345468870756, 28243366880391533588057461/203054856288771096)
(284407696170298969/1167359237136, 231824051495857326801620861/1261266283608168384)
(6892775845248521/21621937936, 723044537972563495314427/3179376241861184)
(630916065212308649/1731545437924, 592833489694864521547726473/2278509473946308968)
(51476965986458649669209/11513978017878436, 11680632461119089696039820826086169/1235486755131881501065816)
(77063440088221277009/275326985280400, 927865650662634473544470606777/4568495160217971592000)
(-33616276035534284234897159/325878573421582266276, 794162196047209382009070679881560133577/5882794933116630955472157864024)
(-422959763471852191895581351/2095528285935126540304, 10106186333044362534921871112541515735997/95926873761904632220353133846592)
(3052241894561201426464279001/747573048403880410000, 168651443103410024552984308598054958637251/20439979393291650964678661000000)
(1319328167930417330157978266274555049/4390738550128646094924898502724, 1982930082792287337337328081295534234355711926235342177/9200392731827541967316747343497333557676440632)

Commentary

The rational 3-isogenous partner of our accepted rank-11 Mordell curve obtained from the Burkhardt quartic with parameters (u,v,w) = (-2,6,-4), specialized at t = 67/404.

last edited by jesper-petersen at 2026-10-23 21:44:04 UTC · history